My front doors have several small hairline cracks around the door panels. I would like to seal them. Can I use clear silicone caulking without damage to the stained surface? Do I need to clean or prep the wood surface for better adhesion?
I don't see any reason why you couldn't use silicon caulking or why it would damage the surface. Just know that you will not be able to stain over it again. Some caulk is listed as paintable which might be a better bet as at least you can paint it down the road if you choose.
If you are going to want to stain the door at a later date, a wood filler product would probably work best as it will blend in well and accept the stain.
As for cleaning the door, you definitely want to remove any dirt and debris from the area you are going to fix. You will want to scrape off and remove any previous caulking that may be present too.